Epigraphically-Relaxed Linearly-Involved Generalized Moreau-Enhanced Model for Layered Mixed Norm Regularization

Akari Katsuma, Seisuke Kyochi, Shunsuke Ono, Ivan Selesnick

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper proposes an epigraphically-relaxed linearly-involved generalized Moreau-enhanced (ER-LiGME) model for layered mixed norm regularization. Group sparse and low-rank (GSpLr)-aware modeling using ℓ1 /nuclear-norm-based layered mixed norms has succeeded in precise high dimensional signal recovery, e.g., images and videos. Our previous work significantly expands the potential of the GSpLr-aware modeling by epigraphical relaxation (ER). It enables us to handle a (even non-proximable) deeply-layered mixed norm minimization by decoupling it into a norm and multiple epigraphical constraints (if each proximity operator is available). One problem with typical SpLr modeling is that it suffers from the underestimation effect due to the ℓ1 and nuclear norm regularization. To circumvent this problem, LiGME penalty functions, which modify conventional sparsity and low-rankness promoting convex functions to nonconvex ones while keeping overall convexity, have been proposed conventionally. In this work, we integrate the ER technique with the LiGME model to realize deeply-layered (possibly non-proximable) mixed norm regularization and show its effectiveness in denoising and compressed sensing reconstruction.

Original languageEnglish (US)
Title of host publication2023 IEEE International Conference on Image Processing, ICIP 2023 - Proceedings
PublisherIEEE Computer Society
Pages2240-2244
Number of pages5
ISBN (Electronic)9781728198354
DOIs
StatePublished - 2023
Event30th IEEE International Conference on Image Processing, ICIP 2023 - Kuala Lumpur, Malaysia
Duration: Oct 8 2023Oct 11 2023

Publication series

NameProceedings - International Conference on Image Processing, ICIP
ISSN (Print)1522-4880

Conference

Conference30th IEEE International Conference on Image Processing, ICIP 2023
Country/TerritoryMalaysia
CityKuala Lumpur
Period10/8/2310/11/23

Keywords

  • Convex optimization
  • epigraphical projection
  • LiGME model
  • signal recovery
  • structure tensor total variation

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Signal Processing

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